Making mirrored object a real object with mesh
The Mirror Modifier has a Merge option.  



DO untick that! - check that the checkbox is not checked, so you have to separate objects while working with the Mirror.
Now the Magic:
After applying the Mirror modifier, you can go into edit mode and use "L" in Face select mode to "select linked".
that means you select all facees that are connected and because you dont merged before you can select both halfs of the mirror separatly.
Now pres "P" to separate selected. leave edit mode.

now you have two objects and can go one with it.